package batteries

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Module BatFingerTree

This module implements a generic finger tree datastructure as described here: Finger Trees: A Simple General-purpose Data Structure http://www.soi.city.ac.uk/~ross/papers/FingerTree.pdf

The finger tree itself is polymorphic over the measure and the measurement function (this is needed because sometimes the type of the measure depends on the type of the elements).

This module also contains an instantiation of a finger tree that implements a functional sequence with the following characteristics:

  • amortized constant time addition and deletions at both ends
  • constant time size operation
  • logarithmic lookup, update or deletion of the element at a given index
  • logarithmic splitting and concatenation

If you are trying to understand the signature at first, whenever you see a type (something, _, _) wrap, just pretend it is simply the type something (this is what the documentation does).

Complexities are given assuming that the monoid combination operation and the measurement functions are constant time and space.

None of the functions on finger trees can cause stack overflow: they use at worst a logarithmic amount of stack space.

type 'a monoid = {
  1. zero : 'a;
    (*

    The neutral element of the monoid.

    *)
  2. combine : 'a -> 'a -> 'a;
    (*

    combine should be associative, and have zero as neutral element.

    *)
}

The type of the element of a monoid.

exception Empty

An exception that is thrown by various operations when trying to get a non existing element.

module type S = sig ... end
module Generic : sig ... end
type 'a t
include S with type ('wrapped_type, 'a, 'm) wrap = 'wrapped_type and type ('a, 'm) fg = 'a t
type ('a, 'm) fg = 'a t

The type of finger trees containing elements of type 'a measured by 'm.

type ('wrapped_type, 'a, 'm) wrap = 'wrapped_type

A type meant to avoid duplication of signatures.

For the generic finger tree, this type will be monoid:'m monoid -> measure:('a -> 'm) -> 'wrapped_type.

Once the finger tree has been specialized, the resulting module should be reexported in such a way that the type is now simply 'wrapped_type.

Construction
val empty : ('a, 'm) fg

empty is the sequence with no elements.

val singleton : 'a -> ('a, 'm) fg

singleton elt build the sequence containing elt as its sole element.

O(1).

val cons : (('a, 'm) fg -> 'a -> ('a, 'm) fg, 'a, 'm) wrap

cons t elt adds elt to the left of t.

O(1) amortized, O(log(n)) worst case.

val snoc : (('a, 'm) fg -> 'a -> ('a, 'm) fg, 'a, 'm) wrap

snoc t elt adds elt to the right of t.

O(1) amortized, O(log(n)) worst case.

Deconstruction
val front : (('a, 'm) fg -> (('a, 'm) fg * 'a) option, 'a, 'm) wrap

front t returns None when t is empty, or Some (tl, hd) when hd is the first element of the sequence and tl is the rest of the sequence.

O(1) amortized, O(log(n)) worst case.

val front_exn : (('a, 'm) fg -> ('a, 'm) fg * 'a, 'a, 'm) wrap

front_exn t returns (tl, hd) when hd is the first element of the sequence and tl is the rest of the sequence.

  • raises Empty

    if t is empty.

O(1) amortized, O(log(n)) worst case.

val head : ('a, 'm) fg -> 'a option

head t returns None if t is empty, or Some hd otherwise, where hd is the first element of the sequence.

O(1).

val head_exn : ('a, 'm) fg -> 'a

head_exn t returns the first element of the sequence.

  • raises Empty

    if t is empty.

O(1).

val last : ('a, 'm) fg -> 'a option

last t returns None if t is empty, or Some hd otherwise, where hd is the last element of the sequence.

O(1).

val last_exn : ('a, 'm) fg -> 'a

last_exn t returns the last element of the sequence.

  • raises Empty

    if t is empty.

O(1).

val tail : (('a, 'm) fg -> ('a, 'm) fg option, 'a, 'm) wrap

tail t returns None when t is empty, or Some tl where tl is the sequence t where the first element has been removed.

O(1) amortized, O(log(n)) worst case.

val tail_exn : (('a, 'm) fg -> ('a, 'm) fg, 'a, 'm) wrap

tail_exn t returns the sequence t where the first element has been removed.

  • raises Empty

    if t is empty.

O(1) amortized, O(log(n)) worst case.

val init : (('a, 'm) fg -> ('a, 'm) fg option, 'a, 'm) wrap

init t returns None if t is empty, or Some init where init is the sequence t where the last element has been removed.

O(1) amortized, O(log(n)) worst case.

val init_exn : (('a, 'm) fg -> ('a, 'm) fg, 'a, 'm) wrap

init_exn t returns the sequence t where the last element has been removed.

  • raises Empty

    if t is empty.

O(1) amortized, O(log(n)) worst case.

val rear : (('a, 'm) fg -> (('a, 'm) fg * 'a) option, 'a, 'm) wrap

rear t returns None when t is empty, or Some (init, last) where last is the last element of the sequence and init is the rest of the sequence.

O(1) amortized, O(log(n)) worst case.

val rear_exn : (('a, 'm) fg -> ('a, 'm) fg * 'a, 'a, 'm) wrap

rear_exn t returns (init, last) when last is the last element of the sequence and init is the rest of the sequence.

  • raises Empty

    if t is empty.

O(1) amortized, O(log(n)) worst case.

Inspection
val is_empty : ('a, 'm) fg -> bool

is_empty t returns true when the sequence has no elements.

O(1).

val fold_left : ('acc -> 'a -> 'acc) -> 'acc -> ('a, 'm) fg -> 'acc

fold_left is equivalent to List.fold_left.

O(n).

val fold_right : ('acc -> 'a -> 'acc) -> 'acc -> ('a, 'm) fg -> 'acc

fold_right is equivalent to List.fold_right.

O(n).

val iter : ('a -> unit) -> ('a, 'm) fg -> unit

iter is equivalent to List.iter.

O(n).

val iter_right : ('a -> unit) -> ('a, 'm) fg -> unit

iter_right is equivalent to List.iter o List.rev.

O(n).

val compare : ('a -> 'a -> int) -> ('a, 'm) fg -> ('a, 'm) fg -> int

compare cmp t1 t2 compares the two sequences lexicographically.

O(n).

val equal : ('a -> 'a -> bool) -> ('a, 'm) fg -> ('a, 'm) fg -> bool

equal eq t1 t2 returns true when the two sequences contain the the same elements.

O(n).

Conversions
Conversions to other structures
val enum : ('a, 'm) fg -> 'a BatEnum.t

enum t builds an enumeration of the elements of t going from left to right.

O(1).

Forcing the whole enumeration takes O(n).

val backwards : ('a, 'm) fg -> 'a BatEnum.t

backwards t builds an enumeration of the elements of t going from right to left. Same complexity as enum.

val to_list : ('a, 'm) fg -> 'a list

to_list t is equivalent to BatList.of_enum (enum t).

O(n).

val to_list_backwards : ('a, 'm) fg -> 'a list

to_list_backwards t is equivalent to BatList.of_enum (backwards t).

O(n).

Conversions from other structures
val of_enum : ('a BatEnum.t -> ('a, 'm) fg, 'a, 'm) wrap

of_enum e build the sequence containing the elements of e in the same order.

Its complexity is the complexity of forcing the enumeration.

val of_backwards : ('a BatEnum.t -> ('a, 'm) fg, 'a, 'm) wrap

of_backwards e is equivalent to reverse (of_enum e).

O(n).

val of_list : ('a list -> ('a, 'm) fg, 'a, 'm) wrap

of_list l is equivalent to of_enum (BatList.enum l).

O(n).

val of_list_backwards : ('a list -> ('a, 'm) fg, 'a, 'm) wrap

of_list_backwards l is equivalent to of_enum_backwards (BatList.enum l).

O(n).

Combining/reorganizing
val map : (('a -> 'b) -> ('a, 'm) fg -> ('b, 'm) fg, 'b, 'm) wrap

map is equivalent to List.map.

O(n).

val map_right : (('a -> 'b) -> ('a, 'm) fg -> ('b, 'm) fg, 'b, 'm) wrap

map_right is equivalent to List.rev o List.map o List.rev.

O(n).

val append : (('a, 'm) fg -> ('a, 'm) fg -> ('a, 'm) fg, 'a, 'm) wrap

append is equivalent to List.append.

O(log(min(n,m))).

val reverse : (('a, 'm) fg -> ('a, 'm) fg, 'a, 'm) wrap

reverse t is equivalent to of_list (List.rev (to_list t)).

O(n).

Boilerplate code
val print : ?first:string -> ?last:string -> ?sep:string -> ('a, 'b) BatIO.printer -> (('a, _) fg, 'b) BatIO.printer
val size : 'a t -> int

size t returns the number of elements in the sequence.

Unlike the generic size on finger trees, this one has complexity O(1).

val split_at : 'a t -> int -> 'a t * 'a t

split_at is equivalent to List.split_at.

O(log(n)).

val get : 'a t -> int -> 'a

get t i returns the i-th element of t.

O(log(n)).

val set : 'a t -> int -> 'a -> 'a t

set t i v returns t where the i-th element is now v.

O(log(n)).

val update : 'a t -> int -> ('a -> 'a) -> 'a t

update t i f returns t where the i-th element is now f (get i t).

O(log(n)).